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The Hellmann-Feynman, virial and comparison theorems are three fundamental theorems of quantum mechanics. For the first two, counterparts exist for classical mechanics with relativistic or nonrelativistic kinetic energy. It is shown here…
The so-called ``analogue models of general relativity'' provide a number of specific physical systems, well outside the traditional realm of general relativity, that nevertheless are well-described by the differential geometry of curved…
A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic…
Concepts and formalism from acoustics are often used to exemplify quantum mechanics. Conversely, quantum mechanics could be used to achieve a new perspective on acoustics, as shown by Gabor studies. Here, we focus in particular on the study…
We study sound in a single-channel one-dimensional quantum liquid. In contrast to classical fluids, instead of a single sound mode we find two modes of density oscillations. The speeds at which these two sound modes propagate are nearly…
A new analogy between superfluid systems and cosmology is here presented, which relies strongly on the following ingredient: the back-reaction of the vacuum to the quanta of sound waves. We show how the presence of thermal phonons, the…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
The landscape of causal relations that can hold among a set of systems in quantum theory is richer than in classical physics. In particular, a pair of time-ordered systems can be related as cause and effect or as the effects of a common…
Out of several possible extensions of general relativity, the scalar-tensor theory is the most popular for several reasons. Since the quantum description of gravity is yet to be formulated properly, the understanding of a gravitational…
The concept of classical and quantum free acoustic (FA) field is theoretically considered. The equations of the free acoustic field are derived. They coincide in the mathematical form with Maxwell equations for the free electromagnetic (EM)…
A correspondence between scalar field fluctuations and generalized fluctuations in a hydrodynamic approximation of fields is obtained. The results presented here are of interest to field-fluid correspondences and form part of theoretical…
A classical dynamical system in a four-dimensional Euclidean space with universal time is considered. The space is hypothesized to be originally occupied by a uniform substance, pictured as a liquid, which at some time became supercooled.…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin…
The Maxwell equations in the presence of sources are first derived without making use of the potentials and the Hamilton-Jacobi equation for classical electrodynamics is written down. The manifestly gauge invariant theory is then quantized…
Quantum theory is extremely successful in explaining most physical phenomena, and is not contradicted by any experiment. Yet, the theory has many puzzling features : the occurrence of probabilities, the unclear distinction between the…
We consider the sound radiation from an acoustic point-like source moving along a supersonic ("space-like") trajectory in a fluid at rest. We call it an acoustic "tachyonic" source. We describe the radiation emitted by this supersonic…
From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in 4-velocity of the particle. The linear law leads to the vector gauge theory which could be the abelian…
Quantum theory expresses the observable relations between physical properties in terms of probabilities that depend on the specific context described by the "state" of a system. However, the laws of physics that emerge at the macroscopic…
The acoustic fields and streaming in a confined fluid depend strongly on the acoustic boundary layer forming near the wall. The width of this layer is typically much smaller than the bulk length scale set by the geometry or the acoustic…